Question : Which of the following statement(s) is/are TRUE?
I. The total number of positive factors of 72 is 12.
II. The sum of the first 20 odd numbers is 400.
III. The largest two-digit prime number is 97.
Option 1: Only I and II
Option 2: Only II and III
Option 3: Only I and III
Option 4: All are true.
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Correct Answer: All are true.
Solution :
Let's verify each of the statements one by one.
Statement 1:
1. Factors of 72 is 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, i.e., total = 12.
Statement 2:
2. Sum of 20 odd numbers $S = \frac{n}{2}[2a+(n–1)d]$
$S = \frac{20}{2}[2\times1+(20–1)2]$
$S = \frac{20}{2}[2+(19×2)]$
$S = \frac{20}{2}[40]$
$S = 400$
Statement 3:
3. The largest 2-digit prime number nearest to 100 is 97. (A number divisible by only 1 or itself is a prime number.)
So, here all statements are true.
Hence, the correct answer is 'All are true'.
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